Radio communication systems involve the transmission of information over an air interface, for example, by modulating a carrier frequency with the transmitted information. Upon reception, a receiver attempts to accurately extract the information from the received signal by performing an appropriate demodulation technique. However, in order to demodulate a received signal, it is first necessary to synchronize timing between the transmitter and receiver. For example, clocking differences between the transmitter and the receiver provide for differences in bit timing.
Moreover, in some radio communication systems, information is transmitted in bursts, sometimes referred to as “frames”. In these types of systems, it is also desirable to locate the beginning of a frame, so that information relevant to a particular receiver is isolated and demodulated.
Unfortunately, there exists many challenges associated with synchronizing to a received signal. For example, although the receiver may be tuned to an assigned frequency on which its intended signal has been transmitted, Doppler shifting may result in a large frequency offset between the frequency to which the receiver is tuned and the actual frequency of the desired information signal when it reaches the receiver after having traveled through the air interface. Moreover, the crystal oscillator used in the receiver is only accurate to within a certain number of parts per million, which may introduce an additional frequency offset.
In addition to an unknown frequency offset, a receiver must also cope with unknown phase accuracy, i.e., the receiver does not know the difference between the phase of the signal generated by its synthesizer at power-on and the phase of the received signal. Thus, the receiver faces at least three challenges in synchronizing to the received signal: unknown timing, unknown frequency offset and unknown phase. For timing and phase offsets relatively short training sequences can provide satisfactory estimation results. However, short training sequences do not provide satisfactory frequency estimation using current methods.
One method of over coming these challenges, the data aided technique, uses a long training sequence to estimate the frequency parameters. This requires significant overhead and time to train the receiver. For example, burst modems require around 100 symbols to get an accuracy of 10−4 relative to symbol rate at a signal to noise ratio of Es/No=5 dB. Since burst lengths can be as short as 200 symbols, large overheads can be prohibitive and result in reduced throughput.
FIG. 1 is a graph 100 depicting the data-aided Cramer-Rao Bounds for frequency estimation. Specifically, graph 100 shows the theoretical bounds for a modem training sequence where a separate training sequence is communicated with the data. The training sequence is used to synchronize the signal and the data is then capable of being processed by the receiver. The horizontal axis depicts how many symbols are required to be communicated in order to train the receiver while the vertical axis depicts the accuracy of the estimation. As discussed above, the data aided approach reduces, throughput because of the training sequence that must be sent. For example, Internet data can be as short as 200 symbols while the training sequence required would be 100 symbols, which is not efficient because half of the bandwidth is dedicated to the training sequence.
Specifically, FIG. 1 plots the following modified Cramer-Rao bound for frequency estimation which can be represented by the following equation:
                                                        σ              2                        ⁡                          (              f              )                                ≥                                    3                              2                ⁢                                  T                  2                                ⁢                                  π                  2                                ⁢                                  N                  3                                                      ·                          1                                                E                  s                                /                                  N                  0                                                                    ,                            (        1        )            where T is the symbol duration and N is the length of training sequence. The modified Cramer-Rao bound is a lower bound for an unbiased estimator. The bound can be re-arranged as
                              2          ⁢                                          ⁢          π          ⁢                                          ⁢                      σ            ⁡                          (              f              )                                      ≥                                            6                                                N                  3                                ⁢                                                      E                    s                                    /                                      N                    0                                                                                .                                    (        2        )            As can be seen from the FIG. 1, in order to achieve 10−4 accuracy, the training sequence has to be at least 175 symbols at 5 dB Es/No.
FIG. 2 is a graph 200 depicting a non-data aided Cramer-Rao bound for frequency offset. Compared to graph 100, graph 200 shows that training takes much longer to achieve the same accuracies compared to graph 100. The non-data aided approach takes much longer to train a modem. However, the benefit is that the training sequence is not required to be sent since synchronization is done before the data is received. Unfortunately, the time frame for synchronization using the non-data aided approach is prohibitive.
Without knowing the data, as expected, for estimation in the non-data aided case, performance is always poorer than in the data-aided case. Furthermore, non-data aided frequency estimation can be classified into timing aided or non-timing aided. Non-timing aided estimation typically has very poor performance. On the other hand, performance of timing aided estimation deteriorates very quickly if timing estimation becomes less accurate.
Current methodologies such as the data aided and non-data aided approach do not adequately eliminate and/or reduce these challenges to achieve sufficiently accurate synchronization at a high enough first frame success rate in the face of low signal-to-noise ratios. Therefore, it would be advantageous to provide new techniques for synchronizing to a received information signal that overcomes these drawbacks.